Gas streams containing variable compositions of hydrogen and nitrogen are produc

Question

Gas streams containing variable compositions of hydrogen and nitrogen are produced on request by blending gases from two feed tanks. Both tanks themselves contain a mixture of hydrogen and nitrogen. Tank A has a hydrogen mole fraction of 10% and Tank B has a hydrogen mole fraction of 50%. The desired product is a mixture with a hydrogen mole fraction of 20% at a mass flow rate of 100 kg/hr. Find the mass flow rates from each tank, as well as the highest possible hydrogen mole fraction that can be produced from the two tanks.

Explanation / Answer

Average molar mass of gas from:

Tank A=0.1*Mass of hydrogen+0.9*mass of N2

                =0.1*2+0.9*28=25.4 g/mol

Tank B=0.5*2+0.5*28=15g/mol

Stream containing 20% H2=0.2*2+0.8*28=22.8g/mol

Now,

For flow rate of 100 kg/hr

Molar flow rate=100/22.8=4.386 kmol/hr

Let flow rate form tank A be x and tank B be y.

Then we have,

x+y=4.386

and, 0.1x+0.5y=0.2*4.386

Show molar flow rate from:

Tank A=3.2895 kmol/hr

Tank B=1.0965 kmol/hr

Mass flow rate from:

Tank A=Molar flow rate*avg mol wt

                =3.2895*25.4=83.55 kg/sec

Tank B=1.0965*15=16.45 kg/sec

Now highest possible hydrogen mole fraction is if we feed only from tank B.

That is 50% hydrogen is highest possible mole fraction.

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